Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.     

Characteristics of smokeless tobacco use among high school football players as related to type of smokeless tobacco and period of use.

The present study was conducted to assess differences in the behavioral and demographic characteristics of snuff (dip) users as compared to users of chewing tobacco. High School football players (1116) were surveyed concerning their use and perceptions of smokeless tobacco. Adolescent athletes who tried smokeless tobacco were more likely to be white, to use cigarettes, alcohol, and cigars and to have family users than those who never tried. Initial use was highest before the age of fourteen years and was influenced by friends, curiosity and family. Dippers tended to initiate use because of friends, while chewers started because of family users. Users of both dip and chew started primarily because of curiosity. Users of both were more likely to consume greater amounts to alcohol and cigarettes and to smoke cigars and pipes. It appears that the longer smokeless tobacco is consumed, the more likely both dip and chew will be used. Users of smokeless tobacco for more than two years tended to consume more of the product each week, used it for more hours/day, initiated use at an earlier age, and used it more often at school and work than those using it for less than two years. Use of cigars/pipes, consumption of alcohol, and quantity of cigarette consumption increased significantly with longer duration of smokeless tobacco use. Intervention and prevention programs would be helped by understanding differences between users of various smokeless tobacco products and differences related to the duration of use. In addition, further analyses of smokeless tobacco users should study chewers, dippers, and users of both separately.     

DO DRINKERS KNOW WHEN TO SAY WHEN? AN EMPIRICAL ANALYSIS OF DRUNK DRIVING

This paper presents empirical evidence that an individual's decision to drive while drunk is negatively affected by the expected full price of driving drunk. The analysis uses a unique data set containing information on self-reported drunk driving matched to state-level drunk driving policies as well as to state excise taxes on beer. These are hypothesized and found to affect drunk driving. Further, we find interesting racial differences but surprisingly small differences by gender in the effect of socioeconomic and policy variables on drunk driving propensities.     

The Meaning of Work and Love: Career Issues and Interventions

Examining concepts about work and love can help people increase their career success and life satisfaction. Career counselors may initiate this examination by eliciting clients' concepts about work and love. After hearing a client's ideas about work and love, counselors can compare this personal meaning to the social meaning of work and love. When this comparison reveals dysfunctional beliefs about work and love, counselors can link these beliefs to their client's career concerns. Such a linkage typically provokes a cognitive dissonance that motivates clients to modify their beliefs. Counselors can facilitate meaning modification by using client-centered and social influence techniques.     

First Nations and community economic development: a case study

A training project in a northern Canadian community providedan opportunity to examine participatory planning approachesand the meaning of work in First Nations communities. Focusgroups conducted three years after the unsuccessful interventionof a community economic development (CED) project suggest thatcomplex factors such as lack of support from community leadersand rate of pay for workers determine whether CED is alwaysappropriate in northern, First Nations contexts.     

Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.     

Exposure Reconstruction for the TCDD-Exposed NIOSH Cohort Using a Concentration- and Age-Dependent Model of Elimination

Recent studies demonstrating a concentration dependence of elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) suggest that previous estimates of exposure for occupationally exposed cohorts may have underestimated actual exposure, resulting in a potential overestimate of the carcinogenic potency of TCDD in humans based on the mortality data for these cohorts. Using a database on U.S. chemical manufacturing workers potentially exposed to TCDD compiled by the National Institute for Occupational Safety and Health (NIOSH), we evaluated the impact of using a concentration- and age-dependent elimination model (CADM) (Aylward et al., 2005) on estimates of serum lipid area under the curve (AUC) for the NIOSH cohort. These data were used previously by Steenland et al. (2001) in combination with a first-order elimination model with an 8.7-year half-life to estimate cumulative serum lipid concentration (equivalent to AUC) for these workers for use in cancer dose-response assessment. Serum lipid TCDD measurements taken in 1988 for a subset of the cohort were combined with the NIOSH job exposure matrix and work histories to estimate dose rates per unit of exposure score. We evaluated the effect of choices in regression model (regression on untransformed vs. ln-transformed data and inclusion of a nonzero regression intercept) as well as the impact of choices of elimination models and parameters on estimated AUCs for the cohort. Central estimates for dose rate parameters derived from the serum-sampled subcohort were applied with the elimination models to time-specific exposure scores for the entire cohort to generate AUC estimates for all cohort members. Use of the CADM resulted in improved model fits to the serum sampling data compared to the first-order models. Dose rates varied by a factor of 50 among different combinations of elimination model, parameter sets, and regression models. Use of a CADM results in increases of up to five-fold in AUC estimates for the more highly exposed members of the cohort compared to estimates obtained using the first-order model with 8.7-year half-life. This degree of variation in the AUC estimates for this cohort would affect substantially the cancer potency estimates derived from the mortality data from this cohort. Such variability and uncertainty in the reconstructed serum lipid AUC estimates for this cohort, depending on elimination model, parameter set, and regression model, have not been described previously and are critical components in evaluating the dose-response data from the occupationally exposed populations.